Question

the mean of three numbers is 14. two of the numbers are 10 and 6. what is the third number? 22 26 20 18

Explanation:

Step1: Recall the mean formula

The mean $\bar{x}$ of $n$ numbers $x_1, x_2, \dots, x_n$ is given by $\bar{x}=\frac{x_1 + x_2+\dots+x_n}{n}$. Here, $n = 3$, $\bar{x}=14$, $x_1 = 10$, $x_2 = 6$, and we need to find $x_3$.

Step2: Substitute values into the formula

Substitute the known values into the mean formula: $14=\frac{10 + 6+x_3}{3}$.

Step3: Solve for $x_3$

Multiply both sides of the equation by 3: $14\times3=10 + 6+x_3$. Calculate $14\times3 = 42$ and $10+6 = 16$. So the equation becomes $42=16 + x_3$. Subtract 16 from both sides: $x_3=42 - 16=26$.

Answer:

26